Odds and Probability

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Sat Aug 14, 2010 3:03 pm

In an essay competition the odds against competitors A, B, C, D are 2;1, 3;1, 4;1 and 5;1. Find the probability that one of them wins the competition?

A. 11/ 120

B. 114/120

C. 127/150

D. 2/17

E. 135/157

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Last edited by dtweah on Sat Aug 14, 2010 5:12 pm, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Sat Aug 14, 2010 3:03 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sat Aug 14, 2010 4:57 pm

dtweah wrote:In an essay competition the odds against competitors A, B, C, D are 2;1, 3;1, 4;1 and 5;1. Find the probability that one of them wins the competition?

A. 11/ 120

B. 114/120

C. 127/140

D. 2/17

E. 135/157

[spoiler]https://www.greguide.com/Free-GRE-Practi ... est-5.html[/spoiler]

Hi,

if the probability against you winning is 2:1, then you have a 1/3 chance of winning. Applying the same rule to the remaining contestants, they have 1/3, 1/4, 1/5 and 1/6 chances to win.

Since we want the probability of A or B or C or D winning, we ADD the individual probabilities.

So:

1/3 + 1/4 + 1/5 + 1/6

getting a common denominator of 120:

40/120 + 30/120 + 24/120 + 20/120

= 114/120... choose B.

Note, however, that on the real test the answer would be 19/20, since answers are always reduced as much as possible. Another example of a poorly written question from this source (the question itself has ambiguities as well).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Sat Aug 14, 2010 7:29 pm

Stuart Kovinsky wrote:
dtweah wrote:In an essay competition the odds against competitors A, B, C, D are 2;1, 3;1, 4;1 and 5;1. Find the probability that one of them wins the competition?

A. 11/ 120

B. 114/120

C. 127/140

D. 2/17

E. 135/157

[spoiler]https://www.greguide.com/Free-GRE-Practi ... est-5.html[/spoiler]
Hi,

if the probability against you winning is 2:1, then you have a 1/3 chance of winning. Applying the same rule to the remaining contestants, they have 1/3, 1/4, 1/5 and 1/6 chances to win.

Since we want the probability of A or B or C or D winning, we ADD the individual probabilities.

So:

1/3 + 1/4 + 1/5 + 1/6

getting a common denominator of 120:

40/120 + 30/120 + 24/120 + 20/120

= 114/120... choose B.

Note, however, that on the real test the answer would be 19/20, since answers are always reduced as much as possible. Another example of a poorly written question from this source (the question itself has ambiguities as well).

OA different Stuart.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Sat Aug 14, 2010 7:40 pm

dtweah wrote:
OA different Stuart.

Then I'd love to see the OA and explanation - I don't see an error in my approach.

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Sat Aug 14, 2010 11:58 pm

dtweah wrote:
OA different Stuart.

If the OA is different, then find better practice material. Stuart's work is all perfectly correct (as usual!).

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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mainhoon: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Sun Aug 08, 2010 8:36 pm

by mainhoon » Sun Aug 15, 2010 7:35 pm

Ian Stewart wrote:
dtweah wrote:
OA different Stuart.
If the OA is different, then find better practice material. Stuart's work is all perfectly correct (as usual!).

Indeed, the source of material is critical. Especially in the Verbal area! One tends to get more confused than get real answers.. Ian, I have posted a combination question, please take a look and comment.. Thanks

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